A few technology giants dominate their worlds just as Standard Oil and AT&T once did. Should they be broken up?

Standard Oil Co. and American Telephone and Telegraph Co. were the technological titans of their day, commanding more than 80% of their markets.

Today’s tech giants are just as dominant: In the U.S., Alphabet Inc.’s Google drives 89% of internet search; 95% of young adults on the internet use a Facebook Inc. product; and Amazon.com Inc. now accounts for 75% of electronic book sales. Those firms that aren’t monopolists are duopolists: Google and Facebook absorbed 63% of online ad spending last year; Google and Apple Inc. provide...